The Genius Of Joseph Louis Lagrange

The only man who could rival Leonhard Euler in eighteenth century mathematics was Joseph Louis Lagrange. He was born in 1736 into a French family living in Turin, Italy, as one of eleven children; and of these eleven children, only he survived the first few years of life. Already the mathematics of probability were aligning in his favor.

His initial interests in life were literary and philological, especially in the Latin language, but he was directed towards mathematics by the chance reading of some writings by Sir Edmund Halley. His incredible abilities were confirmed when, at the age of nineteen, he sent the mathematical titan Leonhard Euler a new method of analysis for the calculus of variations. Lagrange’s solutions had charted waters that even the old Swiss genius had been unable to navigate. Euler, with a graciousness rare in the history of academics, gave his young admirer full credit for the discovery. He also had Lagrange elected in 1759 as a foreign member of the Berlin Academy.

Lagrange would eventually move to Berlin in 1766. Frederick II, the Prussian king (“The Great”), was a patron of the arts and sciences and was determined to collect a hive of learned men in his capital. It was in Berlin that Lagrange began work on, and completed, his crowning achievement. It was entitled Mecanique analytique, and it would revolutionize nearly every field of scientific endeavor. As a man, Lagrange was moody and depressed. He found consolation in his work, but remained haunted by despair for most of his life.

He found it prudent to leave Berlin upon the death of der Grosse Koenig in 1786; Frederick William II, the new king, was numb to the enchantments of science. So he accepted an invitation to Paris from Louis XVI; there he would join the Academie des Sciences. But political conditions in Paris at the time were teetering on chaos. He had brought the manuscript of his masterpiece with him, but it presented a formidable challenge to a publisher. It was filled with charts, symbols, and other special requirements that only an academic press could handle.

Luckily for history, Lagrange had two supportive friends who found a publisher in the city for him. They convinced the printer to undertake the task of producing the manuscript, but there was a catch: they would have to pay “up front” for the costs of publication. Revolution was not conducive to the purchase of mathematical treatises, and Lagrange had the bad luck of simply being in the wrong place at the wrong time. When the book was finally produced in 1788, he refused to look at it for nearly two years; by this time his depression had come to dominate his life, sapping his energy and draining his vitality.

And yet, by any measure, the work was a masterpiece. Most critics rate it as the equal of Newton’s Principia. Lagrange’s methods of analysis were to use algebraic calculus, rather than older forms of computation and reasoning. He had exploded the field of mechanics and “variations” by producing general formulas that could be applied as needed to particular problems.

But political chaos threatened to overturn his world. France descended into something like anarchy in 1789, and Lagrange, although apolitical himself, feared that mob madness would pay scant attention to the difference between friend and foe. He was greatly disturbed by the execution of his scientific colleague Lavoisier, but chose to remain in France. For some reason, the Jacobins left him alone. Perhaps, not being a nobleman and without much money, he was not viewed as a threat.

He was appointed to head the Ecole Normale in 1795 when it opened. He became one of the leading voices in the establishment of the metric system, and how he chose the new system’s basis of measurement is a pleasant tale. The committee tasked with supervising the new system decided to use a length equal to one ten-millionth of the circle that passed around the earth through the poles. This unit of measurement would be called a “meter.”

Life had a few surprises in store for him. At the age of fifty-six, he attracted the attention of a girl of seventeen years of age; the girl was the daughter of an astronomer friend of his. She adored him, and despite his hesitations, he gave in and married her. It is interesting that in previous ages what was seen as healthy and normal would now be roundly condemned.

He revised his magnum opus (Mecanique analytique) in 1810 for a second edition. These labors caught up with him, and he died in 1813. He, along with Euler, was the greatest mathematician of nineteenth century. A few of his last words were:

…I came to the end without sorrow, without regrets, and by a very gentle decline. Death is not to be dreaded, and when it comes without pain it is a last function which is not unpleasant…Death is the absolute repose of the body.

When we build bridges, scale buildings, launch ships, fire rockets, or apply countless engineering and architectural principles in accord with the aspirations of the mind, we honor Lagrange.